Two-Electron Heisenberg Exchange Interaction between Neighboring Atoms

The method of Nesbet is applied to the model investigated by Freeman and Watson to describe the Heisenberg exchange interaction between neighboring transition metal atoms. Pairs of atomic Hartree-Fock $d$ orbitals obtained from calculations on ${\mathrm{Co}}^{++}$ and Co are used; the nuclei and the remaining electrons are represented by two point charges at the nearest neighbor internuclear separation of Co atoms in the metal. Nuclear charges, $Z$, of one and ten are used to examine the effect of changing the assumed potential. The effective Heisenberg exchange parameter is large and negative for all values of the parameters used here. The present results agree in sign with the earlier results of Freeman and Watson, who used the Heitler-London method without the ionic configuration, but differ by an order of magnitude for $Z=1\mathrm{}$, and are somewhat closer for $Z=10\mathrm{}$. The discrepancy is probably due to this omission, since the present formalism takes all configurations into account for a system described by two basis orbitals. Since the observed exchange parameter for metallic cobalt is positive (ferromagnetic), and since previous investigations suggest that additional effects (due to including the remaining electrons of the ions) will not substantially alter the computed value, it appears that the ferromagnetic coupling must be explained by some mechanism other than the two-atom Heisenberg exchange interaction between localized $d$ orbitals.